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Name: _______________________________

**The Summer Intro Packet is designed for students to review material from their previous mathematics course so they are ready to begin the 8 th**

** grade Introduction to **

**Algebra & Geometry course in the Fall. The expectation is that the concepts contained in the packet are mastered **

*before*

** beginning the Intro course in August. **

*This packet is to be completed by the first day of school. *

**-Show All Work! – enough space has been provided on the packet itself, however, if you do not feel you have enough space to show your work on a given problem, please show your work on a separate sheet of paper. Staple any of your extra work to the packet. **

**-once finished, grade your packet and mark the appropriate box. Corrections should be done in a separate color to show difference **

**-if you need help with a concept, use the **

*phschool.com*

** website to **

** watch the tutorials or practice examples **

**-any of the topics can also be Googled and many tutorials are **

** available online **

**- a quiz will be given on this material the first week of school **

**Be prepared to be successful in 8 th**

** grade math by completing your packet this summer, and making sure you understand all of the concepts within the packet by the first day of class in August. **

**Good Luck! **

Name-Period: ________________________________

**Introduction to Algebra & Geometry Summer Packet**

**Multiple Choice**

*Identify the choice that best completes the statement or answers the question.*

____ 1.

**Identify the expression as a **

*numerical expression*

** or a **

*variable expression*

**. For a variable expression, name the variable.**

7 a. numerical expression b. variable expression;

* d*

is the variable. c. variable expression;

* g *

is the variable. d. variable expression; there is no variable.

____

____

2.

9 a. variable expression;

* i *

is the variable. b. variable expression;

* b*

is the variable. c. numerical expression d. variable expression; there is no variable.

3. Write a variable expression for a number

* x*

divided by 5.

____ a.

*x*

6 b. 5

* – x*

c. 5

*x*

4. Write a word phrase that can be represented by

*k*

– 11. d.

*x*

5 a. 11 more than a number

*k*

b. 11 less than a number

*k*

c. the difference of 11 and

*k*

d. the quotient of a number

*k*

and 11

____

**Compare. Use >, <, or = to complete the statement.**

5. 6

–8

c. <

____

____ a. >

6.

–12

–11 b. = a. < b. >

**Name the property shown.**

7. 4

0 = 4 a. Identity Property of Addition b. Commutative Property of Addition c. Commutative Property of Multiplication d. Associative Property of Addition c. =

____

** Name the property shown. **

8. (9

2)

12 = 9

(2

12) a. Identity Property of Multiplication b. Associative Property of Multiplication c. Commutative Property of Multiplication d. Commutative Property of Addition

____ 9. (6

3)

12 = (3

6

12 a. Commutative Property of Addition b. Associative Property of Addition c. Commutative Property of Multiplication d. Identity Property of Addition

**State whether the number is **

*prime, composite, *

**or **

*neither.*

____ 10. 19 a. neither b. prime

____ 11. 21 a. composite b. neither

____ 12. 1 a. prime b. composite

? ____ 13. Which fraction is equivalent to a. b. c.

____ 14. Which fraction is

*not*

equivalent to a. b.

? c.

**Short Answer**

c. composite c. prime c. neither d. d.

** Simplify. SHOW ALL WORK BELOW OR ON A SEPARATE SHEET OF PAPER.**

17. 9 ∙ (5 + 5) + 3 18.

** Evaluate. SHOW ALL WORK BELOW OR ON A SEPARATE SHEET OF PAPER.**

19. 11

*p*

6, for

*p*

= 5 20.

21. 62

3

*a*

, for

*a*

= 12

** Simplify the expression. SHOW ALL WORK BELOW OR ON A SEPARATE SHEET OF PAPER.**

22. 7

*d*

– 8 + 4

*d*

+ 4 23. 2

*v*

– 5 + 5

*v*

** Use the Distributive Property to multiply. SHOW ALL WORK BELOW OR ON A SEPARATE **

**SHEET OF PAPER.**

24. 4(

*b*

+ 1) 25.

–2(2

*q*

– 1)

26. 27.

**Show how to use mental math to simplify the expression. Think about the properties as shown in #7-9.**

28. (17 + 15) + 83 29. 5

9

2 30. 55 + 29 – 15

**Write an integer for each situation.**

31. $19 lost 32. 8 steps forward 33. 6 floors up

34. During the day the temperature was at night?

. At night, the temperature dropped . What was the temperature

38.

40.

35. The highest location in a certain country is 14,864 feet above sea level. The lowest point in the same country is 141 feet below sea level.

**a. b. **

Find the difference of the two elevations.

A city is 7,642 feet above sea level. Is this elevation closer to the highest point or the lowest point?

**Add or subtract. SHOW ALL WORK BELOW OR ON A SEPARATE SHEET OF PAPER.**

36. 3.71 + 3.7

37. 7.3 – 1.77

39.

41.

42.

**Divide or multiply. SHOW ALL WORK BELOW OR ON A SEPARATE SHEET OF PAPER.**

43. 4

1

3

4

4

5

44.

45. Sue needs cups of flour for a batch of cookies. How many batches can she make with 9 cups of flour?

46.

47.

**Solve each equation. SHOW ALL WORK BELOW OR ON A SEPARATE SHEET OF PAPER **

and

**CHECK ALL SOLUTIONS!**

*p*

+ 7 = 15

**Check: **

*j*

– 5 = –8

**Check:**

**Check:**

48. 12

*d*

= –72

49.

**Check:**

50. 5

*x*

– 5 = 5

51. – 9 = –2

**Check:**

**Check:**

52.

53.

54.

55.

56. What is the prime factorization of 180?

**SHOW ALL WORK BELOW OR ON A SEPARATE SHEET **

**OF PAPER.**

**Find the GCF. SHOW ALL WORK BELOW OR ON A SEPARATE SHEET OF PAPER.**

57. 40 and 45

58. Write in simplest form.

**SHOW ALL WORK.**

59. A seventh-grade class has reached

15

17 its quota. If both classes have the same quota, which class is closer to reaching its quota?

7

8

60. You collect baseball cards. You have 16 out of 34 cards for a particular series (A) and 17 out of 37 cards for another series (B). For which series, A or B, do you have the greater fraction of cards?

**Write the ratio as a fraction in simplest form. SHOW ALL WORK.**

61. 18 to 2

62. In the population of a particular country, the male-to-female ratio is 46 to 54. Write this ratio as a fraction in simplest form.

**SHOW ALL WORK.**

63. Find the cost of 10 notebooks if 3 notebooks cost $1.98.

**SHOW ALL WORK.**

**Write and solve an equation.**

64. You withdrew $100 from the ATM machine. The new balance is $372. What was the original balance

*b*

of your account?

65. Alexa scored 87 on her history test. The test had a multiple-choice section and a short-answer section. Alexa got 74 points on the multiple-choice section. How many points

*p*

did she receive on the short-answer section?

66. Mark wants to buy a skateboard that costs $65. He plans to save $5 per week. How many weeks

*w*

will it take him to save $65?

67. This year, 14,265 people applied to a particular college. The number of applicants increased by 868 from last year. How many people

*p*

applied last year?

68. A baseball bat and 8 baseballs cost $163.25. The bat costs $106.45. What is the cost

*c*

of one baseball?

69. Raymond buys bottles of water at $2.10 each and a large pizza at $12.99. The total cost was $21.39. How many bottles of water

*b*

did he buy?

**Solve the proportion. SHOW ALL WORK BELOW OR ON A SEPARATE SHEET OF PAPER **

and

**CHECK ALL SOLUTIONS!!**

**Check: **

70.

**Check:**

71.

8 th

Grade Introduction to Algebra and Geometry

Answer Key

**Check your answers after completing each section. Check whichever statement applies to you. **

Page 2

**Answer **

**I got it on the 1 st try! **

**I got it with corrections. **

**I have no idea. **

1

2 a b

3

4

5

6 d b c b

7

8 a b

9 a

10 b

11 a

12 c

13 a

14 c

15 -43

16 -19

17 93

18 24

19 49

20 44

21 98

22 11

*d*

– 4

23 7

*v*

– 5

24 4

*b*

+ 4

25 -4

*q*

+ 2

26 6

*x*

+ 50

27 -7

*c*

– 76

28 115

29 90

30 69

31 -19

32 8

33 6

34 -16° F

35 a) 15,005 ft; b) closer to highest point

36 7.41

37 5.53

38

25

33

39

9

3

4

47

48

49

50

40

8

8

9

41

42

43

5

36

1

8

4

20

5

44

3

4

45 3 full batches

46

*p*

= 8

*j d n x*

= -3

= -6

= 77

= 2

51

52

53

54

*x*

= 14

*x*

= -4

*p*

= -3

*w*

= 28

55

*d*

= -9

56 2

2

· 3

2

· 5

57 5

58

8

11

59 7 th grade class

60 Series A

61 9

62

23

37

63 $6.60

64 $472

65 13 points

66 13 weeks

71

67 13,397 people

68 $7.10

69 4 bottles

70

*x*

= 20

*a*

= 20